Table Of ContentLandolt-Börnstein
Numerical Data and Functional Relationships in Science and Technology
New Series / Editor in Chief: W. Martienssen
Group III: Condensed Matter
Volume 33
Diffusion in Semiconductors and
Non-Metallic Solids
Subvolume B1
Diffusion in Non-Metallic Solids (Part 1)
without Volume Diffusion in Oxides
Editor
D.L. Beke
Authors
C.E. Allen, D.L. Beke, F. Bénière, C.M. Bruff, A.V. Chadwick,
G. Erdélyi, F. Faupel, C.H. Hsieh, H. Jain, G. Kroll, Hj. Matzke,
G.E. Murch, V.V. Rondinella, E.G. Seebauer
1 3
Editor
D.L. Beke
Department of Solid State Physics,
L. Kossuth University,
4010 Debrecen, Hungary
Authors
C.E. Allen
Chemical Engineering Department,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801-3792, USA
Surface diffusion on semiconductors (subvolume A, Chap. 7)
Surface diffusion on non-metallic solids (subvolume B1, Chap. 12)
D.L. Beke
Department of Solid State Physics,
L. Kossuth University,
4010 Debrecen, Hungary
General introduction (subvolume A, B1, and B2, Chap. 1)
Dislocation and grain-boundary diffusion in semiconductors and silicides (subvolume A, Chap. 6)
Dislocation and grain-boundary diffusion in non-metallic systems (subvolume B1, Chap. 11)
F. Bénière
Centre National de la Recherche Scientifique CNRS
Groupe Matière Condensée et Matériaux (GMCM),
Université de Rennes,
F-35042 Rennes Cedex, France
Diffusion in alkali and alkaline earth halides (subvolume B1, Chap. 2)
H. Bracht
Institut für Metallforschung,
Universität Münster,
D-48149 Münster, Germany
Diffusion in silicon, germanium and their alloys (subvolume A, Chap. 2)
C.M. Bruff
Department of Mechanical Engineering,
The University of Newcastle,
Callaghan NSW 2308, Australia
Chemical diffusion in bulk inhomogeneous semiconductors (subvolume A, Chap. 5)
Chemical diffusion in bulk inhomogeneous non-metallic compounds (subvolume B1, Chap. 10)
A.V. Chadwick
School of Physical Sciences,
University of Kent at Canterbury,
Canterbury, Kent CT2 7NR, UK
Diffusion in fast-ion conducting solids (subvolume B1, Chap. 3)
Diffusion in molecular solids (subvolume B1, Chap. 8)
F.M. d'Heurle
IBM Research Center,
Yorktown Heights, NY 10598, USA
Royal Institute of Technology, (F.T.E. - KTH)
16440 Kista-Stockholm, Sweden
Diffusion in silicides (subvolume A, Chap. 4)
M.B. Dutt
Government of India
Ministry of Defence (R & D ORGN)
Solid State Physics Laboratory,
Ion Implantation Unit
Delhi-110054, India
Diffusion in compound semiconductors (subvolume A, Chap. 3)
G. Erdélyi
Department of Solid State Physics,
L. Kossuth University,
4010 Debrecen, Hungary
Dislocation and grain-boundary diffusion in semiconductors and silicides (subvolume A, Chap. 6)
Diffusion in miscellaneous ionic substances (subvolume B1, Chap. 4)
Dislocation and grain-boundary diffusion in non-metallic systems (subvolume B1, Chap. 11)
F. Faupel
Technische Fakultät der Christian-Albrechts-Universität zu Kiel,
Lehrstuhl für Materialverbunde,
D-24143 Kiel, Germany
Diffusion in glassy and semicrystalline polymers (subvolume B1, Chap. 9)
P. Gas
Centre National de la Recherche Scientifique CNRS
Laboratoire de Métallurgie,
Université Aix-Marseille III,
F-13397 Marseille Cedex 20, France
Diffusion in silicides (subvolume A, Chap. 4)
C.H. Hsieh
Department of Materials Science and Engineering,
Lehigh University,
Whitaker Laboratory,
Bethlehem, PA 18015-3195, USA
Diffusion in oxide glasses (subvolume B1, Chap. 7)
H. Jain
Department of Materials Science and Engineering,
Lehigh University,
Whitaker Laboratory,
Bethlehem, PA 18015-3195, USA
Diffusion in oxide glasses (subvolume B1, Chap. 7)
G. Kroll
Technische Fakultät der Christian-Albrechts-Universität zu Kiel,
Lehrstuhl für Materialverbunde,
D-24143 Kiel, Germany
Diffusion in glassy and semicrystalline polymers (subvolume B1, Chap. 9)
Hj. Matzke
Europäische Kommission
Generaldirektion GFS
Institut für Transurane (ITU),
Angewandte Physik,
D-76125 Karlsruhe, Germany
Diffusion in carbides, nitrides, hydrides, and borides (subvolume B1, Chap. 5)
C.J.A. Monty
Centre National de la Recherche Scientifique CNRS
Institut de Science et de Génie des Materiaux et Procédés,
Odeillo,
F-66125 Font-Romeu, Cedex, France
Volume Diffusion in oxides (subvolume B2, Chap. 6)
G.E. Murch
Department of Mechanical Engineering,
The University of Newcastle,
Callaghan NSW 2308, Australia
Chemical diffusion in bulk inhomogeneous semiconductors (subvolume A, Chap. 5)
Chemical diffusion in bulk inhomogeneous non-metallic solids (subvolume B1, Chap. 10)
V.V. Rondinella
Europäische Kommission
Generaldirektion GFS
Institut für Transurane (ITU),
Angewandte Physik,
D-76125 Karlsruhe, Germany
Diffusion in carbides, nitrides, hydrides, and borides (subvolume B1, Chap. 5)
E.G. Seebauer
Chemical Engineering Department,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801-3792, USA
Surface diffusion on semiconductors (subvolume A, Chap. 7)
Surface diffusion on non-metallic solids (subvolume B1, Chap. 12)
B.L. Sharma
Government of India
Ministry of Defence (R & D ORGN)
Solid State Physics Laboratory,
Ion Implantation Unit
Delhi-110054, India
Diffusion in compound semiconductors (subvolume A, Chap. 3)
N.A. Stolwijk
Institut für Metallforschung
Universität Münster
D-48149 Münster, Germany
Diffusion in silicon, germanium and their alloys (subvolume A, Chap. 2)
Landolt-Börnstein
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Preface
This volume III/33 of Landolt-Börnstein consists of two subvolumes. Originally we intended to collect all
data on diffusion in non-metalllic solids in one volume, but during the collation and selection of
experimental data it turned out that both the field and the number of data are too large to be compressed
into a single volume only. Thus, finally, it was decided to publish two subvolumes: A on "Diffusion in
Semiconductors" and B on "Diffusion in Non-Metallic Solids". Subvolume A has already been published
in 1998.
To hasten publication of subvolume B the compilations have been printed as the authors completed
their manuscripts. Therefore, and due to the large amount of data in the field of Volume Diffusion in
Oxides the subvolume B is further subdivided into two parts: the present Part 1, containing all data for
Diffusion in Non-Metallic Solids without Volume Diffusion in Oxides and Part 2 containing the data for
Volume Diffusion in Oxides, which is in preparation.
Since a volume on Diffusion in Solid Metals and Alloys (Landolt-Börnstein, New Series, Volume
III/26), edited by H. Mehrer, had already been published in 1990, we wanted to follow its excellent and
clear presentation. We, therefore, hope that these new two subvolumes and the previous one on diffusion
can be considered as a truly complete collection of selected data on diffusion in solids. However, there are
some minor differences between these and the previous volume. First of all, the atomic mechanism of
diffusion in non-metallic solids proved to comprise more complex phenomena than the transport in
metallic systems. Usually, in order to interpret the results, various defects, site preferences and
mechanisms should be taken into account even for bulk diffusion. For example, the importance of self
interstitials, the kick-out and the dissociative mechanism, the role of sources and sinks (surfaces,
dislocations) in the case of volume heterodiffusion in silicon was recognised only at the beginning of the
eighties. Furthermore, the problem of the deviation from stoichiometry (and the effect of the partial
overpressure of components) or the presence of some dopants, (small amounts of which can result in an
extrinsic diffusion regime where the concentration of the diffusion vehicles is determined not by thermal
activation, but, for example by the number of charge compensating vacancies), makes the interpretation of
experimental results more difficult. Secondly, especially in materials important in different technological
applications (semiconductors, different oxides) - because of the practical demand for any data on diffusion
- a huge number of investigations already have been carried out starting in the fifties. In these
measurements some of the possible complications (arising, for example, from sources listed above) were
neglected (e.g. the control of one or more additional parameters was not made) and also in their
interpretation - because of the insufficiency of the relevant theories available at that time - crude
approximations were applied. This situation made the work of the contributing authors very complicated
and time-consuming. This fact, perhaps, can make some delay forgivable in the appearance of these
volumes as compared to our original intent and partly explains that sometimes the extent of the
introductions at certain chapters is longer than would generally be expected.
The critical compilation of data was carried out by 21 experts in diffusion. Subvolume A consists of 6
chapters for the following materials and properties: diffusion in silicon, germanium and their alloys,
diffusion in compound semiconductors, diffusion in silicides, chemical diffusion in bulk inhomogeneous
semiconductors, grain-boundary and dislocation diffusion in semiconductors and silicides and surface
diffusion on semiconductors. Although most of the silicides are not semiconducting, because a number of
them have become integrated in the Si technology and because they were not covered in the previous
volume on diffusion in metallic substances this chapter is included here. Furthermore, there is an
increasing number of measurements on chemical diffusion in thin multilayer systems, and since the vast
majority of them are made on amorphous or crystalline semiconductors (mostly on SixGe1- x multilayers)
these data were collected in the chapter on diffusion in silicon, germanium and their alloys.
The present Subvolume B, Part1 contains 10 chapters on diffusion in alkali and alkaline earth halides,
diffusion in fast-ion conducting solids, diffusion in miscellaneous ionic substances, (borates, chlorates,
molibdenates, niobates, phosphates, silicates and sulfates), diffusion in carbides, hydrides, nitrides and
borides, diffusion in oxide glasses, diffusion in molecular solids, diffusion in glassy and semicrsytalline
polymers, chemical diffusion in bulk inhomogeneous non-metallic compounds, grain-boundary and
dislocation diffusion in non-metallic compounds and surface diffusion on non-metallic solids. All
subvolumes contain the same general introductory chapter acquainting the user with the basic concepts
and experimental methods of the field.
Each subvolume contains an electronic version on CD-ROM which can be used easily in the library and/or
via the campus network at the users working place.
I am very grateful to the authors of the chapters for their co-operation in many details. The excellent
collaboration with the editors-in-chief, O. Madelung and W. Martienssen, and with the editorial staff of
Landolt-Börnstein, in particular with Mrs. H. Hämmer, Dr. R. Poerschke and Dr. H. Seemüller was always
encouraging. I would also like to express my gratitude to all members of the diffusion group of our
Department here in Debrecen and to my secretary for helping me very efficiently during the preparation of
these volumes.
Debrecen, January 1999 Dezsô Beke
ISSN 0942-7988 (Condensed Matter)
ISBN 3-540-62391-4 Springer-Verlag Berlin Heidelberg New York
Library of Congress Cataloging in Publication Data
Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie
Editor in Chief: W. Martienssen
Vol. III/33B1: Editor: D.L. Beke
At head of title: Landolt-Börnstein. Added t.p.: Numerical data and functional relationships in science and technology.
Tables chiefly in English.
Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began
publication in 1950 under title: Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik.
Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag
Includes bibliographies.
1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables.
I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910.
III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology.
QC61.23 502'.12 62-53136
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Ref. p. 10-58] 10 Chemical diffusion in bulk inhomogeneous non-metallic compounds 10-1
10 Chemical diffusion in bulk inhomogeneous nonmetallic
compounds
G.E. MURCH AND C.M. BRUFF
10.1 Introduction
In this chapter data are listed on chemical diffusion coefficients in inhomogeneous nonmetallic
compounds. Only data for essentially ‘bulk’ samples (>~2m m) are presented, thus ‘thin film’ data are not
listed. Chemical diffusion data in semiconductors are presented in subvolume III/33A.
~
The diffusion coefficient D which is measured in a chemical composition gradient, is usually called
the chemical diffusion coefficient or occasionally the mutual or collective diffusion coefficient.
Infrequently it may even be called a ‘self’ diffusion coefficient but this is definitely inconsistent with
general usage which reserves the name self diffusion coefficient for the diffusion coefficient measured in a
tracer gradient or the latter diffusion coefficient divided by the tracer correlation factor. Where there is
diffusion in a diffusion couple such as NiO-MgO where both metal components move the chemical
diffusion coefficient is often termed the interdiffusion coefficient.
For diffusion studies in solids in the present context there are three experimental situations that
commonly occur:
1) A nonstoichiometric compound changes composition. An example would be an oxide such as UO
2+x
changing composition after the partial pressure of oxygen in equilibrium with it has been altered to
some new value. It is usually expected that the new partial pressure would still retain the oxide within
the same phase field. Typically, the chemical diffusion coefficient would be obtained from a weight
change experiment. In this example the change of composition comes about only by diffusion of
oxygen atoms. In oxides such as Fe O the chemical diffusion is controlled by the diffusion of iron
1-x
atoms. In general, diffusion of both atomic species could in principle contribute to the change in
composition but in practice at the temperatures of measurement one atomic component is usually much
slower than the other.
2) Interdiffusion of two compounds from a diffusion couple to form a single phase(s). An example here
would be NiO-MgO. Although it is a ternary system, one component (oxygen) is essentially immobile
and the analysis can be treated in a way very similarly to that for a binary metal couple and the well-
known Boltzmann-Matano analysis can be usefully applied. However, unless the cation vacancy
concentration is a linear function of composition, there must, in fact, be a loss or gain of oxygen by the
crystal. While this does not mean that oxygen diffusion must occur, it does mean that there will be a
volume change with attendant lattice strains which may well affect the measured diffusion coefficients.
In interdiffusion both (metal) components can, and usually do, contribute to diffusion.
Landolt-Börnstein
New Series III/33B1
10-2 10 Chemical diffusion in bulk inhomogeneous non-metallic compounds [Ref. p. 10-58
3) Impurity diffusion in a nonmetallic compound. At the limit of one metallic component approaching
zero in the couple described above the chemical diffusion coefficient approaches the impurity
diffusion coefficient. Ideally, in a formal impurity diffusion experiment, the impurity is present at very
low concentrations, so low that it does not affect the diffusion coefficient of the host or the defect
concentration, ie defect production does not accompany the impurity. When these conditions are
obviously not met, the experiment is strictly a chemical diffusion experiment. Clearly it will be
subjective in some cases as to specify what was actually measured. We have taken the view that if the
author(s) considered the experiment to be a chemical diffusion one then the data are presented here.
Otherwise, the data are listed in the impurity chapter in this volume.
10.2 Use of tables
In many solids the chemical coefficient is conveniently expressed by an Arrhenius-like equation
~ ( )
D = D0 exp - Q RT (1)
where D0 is the pre-exponential factor, sometimes called the frequency factor, Q is the activation enthalpy,
~
R is the ideal gas constant (R = 8.3145J mol-1K-1) and T is the absolute temperature. Since D is usually
considered a composite quantity arising from the diffusion coefficients of the individual components as
well as including a thermodynamic factor, the activation enthalpy Q does not have any useful fundamental
meaning. The Arrhenius form of Eqn. 1 should be considered at best a convenient empirical form
appropriate only over the stated temperature range. Extrapolation outside that range should only be done
with considerable caution. It should also be recognised that low temperature chemical diffusion is
probably frequently dominated by grain boundary diffusion, the quantitative role of which, unlike its
tracer diffusion counterpart, is unfortunately rarely established.
The organisation of the tables in terms of compounds is:
Antimonides
Carbides
Chalcogenides - sulphides and selenides only (see also intercalation compounds)
Halides
Intercalation compounds
Nitrides (see also nuclear materials)
Nuclear materials (U, Th and Pu compounds)
Oxides (see also nuclear materials and intercalation compounds)
Silicates
Silicides
Within each group the metal atoms are listed alphabetically irrespective of nonmetallic element.
Note that for user convenience intercalation compounds and nuclear materials have separate entries.
Landolt-Börnstein
New Series III/33B1
